Embed Size (px)
Citation preview
Full Terms & Conditions of access and use can be found athttp://www.tandfonline.com/action/journalInformation?journalCode=gcry20
Download by: [T&F Internal Users], [ Joshua Bayliss] Date: 10 March 2017, At: 01:22
Crystallography Reviews
ISSN: 0889-311X (Print) 1476-3508 (Online) Journal homepage: http://www.tandfonline.com/loi/gcry20
Some historical extracts relevant to the discoveryand application of the diffraction of X-raysby crystals to contribute to the Centennialcelebration and the International Year ofCrystallography
John R. Helliwell , Alexander J. Blake , John Blunden-Ellis , Moreton Moore &Carl H. Schwalbe
To cite this article: John R. Helliwell , Alexander J. Blake , John Blunden-Ellis , MoretonMoore & Carl H. Schwalbe (2012) Some historical extracts relevant to the discovery andapplication of the diffraction of X-rays by crystals to contribute to the Centennial celebrationand the International Year of Crystallography, Crystallography Reviews, 18:1, 3-19, DOI:10.1080/0889311X.2011.641958
To link to this article: http://dx.doi.org/10.1080/0889311X.2011.641958
Published online: 16 Dec 2011.
Submit your article to this journal
Article views: 788
View related articles
Citing articles: 3 View citing articles
Crystallography ReviewsVol. 18, No. 1, January 2012, 3–19
Some historical extracts relevant to the discovery and application of the
diffraction of X-rays by crystals to contribute to the Centennial
celebration and the International Year of Crystallography
John R. Helliwella*, Alexander J. Blakeb, John Blunden-Ellisc,Moreton Moored and Carl H. Schwalbee
aSchool of Chemistry, University of Manchester, Manchester, M13 9PL, UK; bSchool ofChemistry, The University of Nottingham, Nottingham NG7 2RD, UK; cFaculty Team
Manager, Engineering and Physical Sciences, John Rylands University Library, University ofManchester, Manchester M13 9PL, UK; dDepartment of Physics, Royal Holloway University ofLondon, Egham, Surrey TW20 0EX, UK; eSchool of Life and Health Sciences, Aston University,
Birmingham B4 7ET, UK
(Received 8 November 2011; final version received 15 November 2011)
Illustrative extracts from the writings of Paul P. Ewald and of Max von Laue arepresented. The latter in turn contains extensive text contributions from WilliamLawrence Bragg. These selections we have chosen so as to indicate the nature ofthe discovery of X-ray diffraction from crystals (experiments undertaken byFriedrich, Knipping and von Laue) and its early and prompt application incrystal structure analyses (by William Henry Bragg and William LawrenceBragg). The platform for these discoveries was provided by a macroscopic physicsproblem dealt with by Ewald in his doctoral thesis with Arnold Sommerfeld in theMunich Physics Department, which is also where von Laue was based.W.L. Bragg was a student in Cambridge who used Trinity College Cambridgeas his address on his early papers; experimental work was done by him in theCavendish Laboratory, Cambridge, and also with his father, W.H. Bragg, in theLeeds University Physics Department. Of further historical interest is the awardof an Honorary DSc (Doctor of Science) degree in 1936 to Max von Laue by theUniversity of Manchester, UK, while William Lawrence Bragg was LangworthyProfessor of Physics there.
Keywords: Centennial celebration; discovery of X-ray diffraction; Paul Ewaldwritings; Max von Laue writings; William Lawrence Bragg writings; honoraryDSc for von Laue
Contents page
1. Introduction 4
2. Extracts from Paul Ewald’s writings [1] 4
3. Extract from Max von Laue’s writings [2] 7
*Corresponding author. Email: [email protected]
ISSN 0889–311X print/ISSN 1476–3508 online
� 2012 Taylor & Francis
http://dx.doi.org/10.1080/0889311X.2011.641958
http://www.tandfonline.com
4. Short postscripts 13
5. Concluding remarks; glimpses of the interactions between Max von Laue and
William Lawrence Bragg 14
6. Honouring the Centennial 16
Authors’ Biographical sketches 17
Acknowledgements 18
References 19
1. Introduction
Although X-rays had already been discovered by Wilhelm Conrad Rontgen in 1895 andwere immediately used for imaging, their nature was not properly understood for well over adecade. The platform for understanding and applying X-ray diffraction was provided by amacroscopic physics problem dealt with by Paul Peter Ewald in his doctoral thesissupervised by Arnold Sommerfeld in the Physics Department of the University of Munich.Ewald’s conversation about his thesis topic with Max von Laue, who was Sommerfeld’sdeputy, prompted von Laue to speculate whether X-rays could interact with crystals, and topersuade Paul Knipping and Walter Friedrich to join in carrying out experiments. Theirresults were soon communicated to William Henry Bragg and his son William LawrenceBragg, who developed the science of crystal structure determination. W.L. Bragg was astudent in Cambridge who used Trinity College Cambridge as his address on his earlypapers; experimental work was done by him in the Cavendish Laboratory, Cambridge, andalso with his father, W.H. Bragg, in the Physics Department of the University of Leeds.
We present extracts from the writings of Ewald and von Laue that provide acomprehensive description of the background to and development of X-ray crystallogra-phy. An additional question concerns the personal relationship between von Laue and theBraggs. One might expect that a certain amount of scientific rivalry could have existed,exacerbated by the fact that during World War I von Laue worked on militarycommunications for the German army, while W.H. Bragg worked on submarine detectionfor the British Admiralty and W.L. Bragg developed sound ranging techniques for thelocation of guns. However, the evidence is that these great men maintained the highestregard for each other, and von Laue’s text includes important contributions fromW.L. Bragg.
2. Extracts from Paul Ewald’s writings (1)
Reproduced with the permission of the International Union of Crystallography (IUCr):Paul Ewald Chapter 4 ‘Laue’s Discovery of X-ray diffraction by Crystals’ in Fifty
Years of X-ray Diffraction P.P. Ewald Editor, Published for the IUCr by N.V.A.Oosthoek, Utrecht, The Netherlands.
Extracted from Section 4.2 Ewald’s Thesis:Towards the end of the summer semester of 1910 the present author, Paul Ewald, had
belonged to the group of students centering about Sommerfeld [in the Institute for
4 J.R. Helliwell et al.
Theoretical Physics of the University of Munich] for about two years, and he felt that he
could venture to ask his teacher to accept him as a doctorand. . . .At the end of
[Sommerfeld’s] list stood the problem: ‘To find the optical properties of an anisotropic
arrangement of isotropic resonators’. Sommerfeld presented this last topic with the excuse
that he should perhaps not have added it to the others [there being ten or twelve other
topics suitable for doctoral theses] since he had no definite idea of how to tackle it, whereas
the other problems were solved by standard methods of which he had experience. In spite
of the warning, Ewald was immediately struck by the last topic on the list, and even if he
politely postponed the decision to the next appointment a few days later, he went home
determined that it would be this topic or none. When this was agreed to, at the second
interview, Sommerfeld gave Ewald a reprint of Planck’s paper on the Theory of Dispersion
(Berlin Academy 1902), and recommended him to study H. A. Lorentz’s corresponding
paper . . ..It should not be assumed that the division of the problem into that of dispersion and
that of refraction was understood at the beginning of Ewald’s investigation – it developed
clearly only in the course of the work. What Sommerfeld had in mind was this: in Planck’s
and also in Lorentz’s then known work, an amorphous medium had been assumed,
characterized by a random distribution of the resonators in space. This led, naturally, to a
single value of the refractive index, valid for all directions of the light ray travelling
through the medium. If the same type of resonators were placed in a lattice array, with
perfect regularity but different distances along the three coordinate axes – would the
dispersive and refractive properties of this medium be those of a crystal? Would there
result, for a general direction of propagation, two refractive indices whose magnitude
depends on the direction and the polarization of the wave? In other words, would it be
unnecessary to assume an inherent anisotropy of the resonators themselves for the
explanation of crystal optics? These were the questions which preoccupied the author in
the next two years. Heavy mathematics was involved in finding a general answer, and
again in transforming this answer to a form where the magnitude of the effect could be
calculated. All this mathematical technique was, much later, recognized as Fourier
transformation – a concept which had not yet been formed at the time – with the result
that nowadays the mathematical derivations can be presented to a class of graduates in a
two-hour session without undue strain. The model used for the theory was a simple
orthorhombic lattice of isotropic resonators (or dipoles as they are also called); the
positions of the resonators along the x, y, z Cartesian coordinate axes are X, Y, Z¼ la, mb,
nc, where l, m and n are integers ranging independently from �1 to þ1 and a, b, c are
the axes or transformations of the lattice.Ewald showed that the model fulfilled the general laws of crystal optics. In order to
check on the magnitude of the effect, he took, on the advice of Groth, the axial ratios of
anhydrite (CaSO4), a:b:c¼ 0.8932 : 1 : 1.0008. The result of the calculation was that in two
directions, the double refraction of the model was 3–4 times the observed one, and in the
third direction, it was six times smaller. Since no crystal structures were known at the time
and it seemed unlikely that the resonators representing anhydrite should really have the
simple arrangement assumed, an agreement between the observed and calculated values
would have been most unexpected. The conclusion drawn from the calculation was,
however, that the structural anisotropy was ample for producing double refraction of the
observed magnitude, and that in any case would have to be taken into account before
ascribing an inherent anisotropy to the molecular resonators.
Crystallography Reviews 5
Ewald had finished his calculations and was writing out the thesis during the Christmasrecess 1911 and in January 1912. In paragraph 3 of his presentation, he stated theastonishing conclusion that his theory of dispersion, dealing with an unbounded crystal,had no use for an incident ray, even though this played a significant role in the existingtheories of dispersion. The refractive index, like the proper frequency of a mechanicalsystem, was determined by a free vibration of the whole system, without the need of anyexternal excitation. Thence, he concluded that in a bounded system, for instance, a crystallattice filling only the lower half of space, the incident wave must be shielded from theinterior by action of the boundary, so as to allow the establishment of the self-supportingfree vibration.
This conclusion was only later confirmed by direct calculation, in a sequel to theabbreviated re-publication of his thesis in Annalen der Physik 1916, Vol. 49, pp. 1–38 and117–143. At the time of writing the thesis, it seemed a rather radical departure from thetraditional theory. For this reason, Ewald meant to discuss it with Laue who had a strongleaning towards fundamental physics issues.
4.3 Laue’s IntuitionTransposed from page 34:
In the fall of 1909 Laue joined Sommerfeld’s group. He was a pupil of Planck and hadobtained his degree in Berlin. After two post-doctoral years in Gottingen, he returned asassistant of Planck’s to Berlin and became lecturer there for two years. He was Planck’sfavorite disciple, but for some personal or other reason he asked for being transferred toMunich University and this was arranged. Unmarried, and devoted to Physics as he was,he soon became a leading member in all the group’s activities. His interests covered thewhole of physics; he wrote the first monograph on the (special) Theory of Relativity,brought from his association with Planck a deep understanding of thermodynamics andthe theory of radiation and had done some profound thinking on Optics.
Resuming from page 40 onwards:Laue suggested that they (he and Ewald) meet the next day – it was probably late in
January 1912 – in the Institute and discuss before and after supper at his home. They metas arranged and took a detour through the Englische Garten, a park whose entrance wasnot far from the University. After having crossed the traffic on the Ludwigsstrasse, Ewaldbegan telling Laue of the general problem he had been working on, because, to hisastonishment, Laue had no knowledge of the problem. He explained how, in contrast tothe usual theory of dispersion he assumed the resonators to be situated in a lattice array.Laue asked for the reason of this assumption. Ewald answered that crystals were thoughtto have such internal regularity. This seemed new to Laue. Meanwhile they were enteringthe park, when Laue asked: ‘‘What is the distance between the resonators?’’ To this Ewaldanswered that it was very small compared with the wavelength of visible light, perhaps 1/500 or 1/1000 of the wavelength, but that an exact value could not be given because of theunknown nature of the ‘molecules integrantes’ or ‘particles’ of the structure theory; that,however, the exact distance was immaterial for his problem because it was sufficient toknow that it was only a minute fraction of the wave-length.
On the rest of the way, Ewald explained the technique of his treatment of the problem,leaving his main question over for the resumption of the conversation after supper. Whenthe time came, he found Laue listening in a slightly distracted way. He again insisted onknowing the distances between the resonators, and when he received the same answer as
6 J.R. Helliwell et al.
before, he asked: ‘What would happen if you assumed very much shorter waves to travel inthe crystal?’ Ewald turned to paragraph 6, Formula 7, of his thesis manuscript, saying:
‘‘This formula shows the result of the superposition of all wavelets issuing from theresonators. It has been derived without any neglection or approximation and is thereforevalid also for short wave-lengths. It only requires to be discussed for that case. – I,however, have to get my thesis delivered within the next few days and have then to dosome reviewing for my oral examination – you are welcome to discuss the formula which Iam copying out for you’’.
. . . [subsequently] Over these events and the offers of two tempting jobs as assistant(either to Haber or to Hilbert) he forgot about Laue’s interest in the passage of very shortwaves through a crystal. The next he heard of it was a report on Laue-Friedrich-Knipping’s successful experiments which Sommerfeld gave to the Physical Society ofGottingen in June 1912. On coming home from it, Ewald at last looked at the formularecommended to Laue and found the same evening the obvious way of interpreting itgeometrically for short waves by means of a lattice having translations proportional to 1/a,1/b, 1/c, which he called the ‘reciprocal lattice’, and a sphere determined by the mode ofincidence of the X-rays on the crystal, which in English is called ‘sphere of reflection’. Thepaper containing this discussion appeared in Physikalische Zeitschrift 1913, vol. 14, pg.465-472, and its equation (8) is the formula of the thesis recommended to Laue’s attentionbut of which he never made use.
3. Extract from Max von Laue’s writings (2)
From International Tables for X-ray Crystallography Volume 1 with the permission of theIUCr:
HISTORICAL INTRODUCTIONby M. Von Laue
The science which the International Tables are intended to serve is concerned primarilywith the atomic theory of crystals, and secondarily with optical theory as applied to theshort wavelengths of X-radiation. Moreover, now that we know of electron and neutrondiffraction by crystals, it must include quantum mechanical wave theory, which is also, asit happens, of importance in the branch of optics already mentioned. This introduction hasto deal, therefore, with the history of these three branches of physics. Let us begin with themost important and the oldest branch, the theory of crystals.
We may take as a beginning the small pamphlet written in the year 1611 by the greatastronomer Johannes Kepler, which bears the title Strena seu de nive sexangula, or intranslation ‘A New Year’s present; on hexagonal snow’. It is dedicated to one of hispatrons at the court of the Emperor Rudolph II, whose friendship Kepler enjoyed duringhis stay in Prague. Kepler’s astronomical works show that throughout his life he believedthat the material world was the creation of a Spirit delighting in harmony andmathematical order. Had he not tried in his youth to deduce the radii of the planetaryorbits from the dimensions of certain regular polyhedra, and did not his principal work(1619) bear the title Harmonice Mundi? It need not surprise us, therefore, that it was theappearance of these regular and beautifully shaped snowflakes rather than the appearanceof the crystals of the mineral world that inspired Kepler with the idea that this regularitymight be due to the regular geometrical arrangement of minute and equal brick-like units.
Crystallography Reviews 7
Thus, he was led to think of close-packed spheres, and, although he did not coin theexpression ‘space-lattice’ and although his development of these ideas is not alwayscorrect, we can find among his illustrations the first pictures of space-lattices.
Nevertheless, Kepler felt uneasy about these speculations. He realized, quite correctly,that his way would lead to an atomic theory; yet, the idea of the atom, as handed downfrom the ancient Greeks, lacked an empirical foundation and therefore has often been thesubject of excessively fanciful speculation even until well into the nineteenth century.Hence, it was not without reason that the natural scientist in Kepler mistrusted this ideaand would not take it seriously. He toyed with the double meaning of the word ‘nix’, whichin Latin means snow but in German dialect ‘nichts’—nothing. And so from beginning toend, he repeatedly explained the whole idea away as a mere ‘nothing’.
In these circumstances, the little pamphlet, even though it was printed, naturally madeno deep impression on his contemporaries, and was gradually forgotten. Crystallographytook another direction, that of the description of the external form of crystals, after NeilsStensen had in 1669 pointed out the existence of characteristic angles between crystal faces.By devious ways, this led eventually to the Millerian indexing of faces (1839), to the laws ofsymmetry and to the classification of crystals in 32 classes, which was accomplished in1830 by Johann Friedrich Christian Hessel, and in 1867, independently and rather moresimply, by Axel Gadolin.
This consistently phenomenological approach was not abandoned, even though thecrystal-optical discoveries made early in the nineteenth century by such men as BaptisteBiot, David Brewster, Augustin Fresnel and Frederick William Herschel had led to thedevelopment of the important idea that the same laws of symmetry which were valid forthe positions of crystal faces also controlled the physical events inside the crystal. This wasfirst made clear by Franz Neumann in 1833.
Apart from these trends of thought, however, ideas about the internal structure ofcrystals continued to appear. Thus, Christiaan Huygens’ fundamental work on the wavetheory of optics, Traite de la lumiere, which was published in 1690, contains among otherthings a wave-theoretical explanation of birefringence, and ascribes to calcite a structuremade up of ellipsoidal particles; the threefold periodicity of this arrangement characterizesit as a space-lattice, although Huygens, like Kepler, did not define it as such. It was thecleavage along three planes which led him to this idea. Like Kepler’s pamphlet, however,this part of the otherwise famous work was soon forgotten. Independently of Huygens,crystal cleavage in general led Torbern Bergman in 1773 and Rene Just Hauy in 1782 tosuppose that all crystals consist of a kind of masonry of equal, parallelepipedal buildingbricks. That these ‘molecules soustractives’ were often supposed to consist of ‘moleculesintegrantes’ of other shapes need not concern us here. A structure of this kind involves aspace-lattice, and Hauy could therefore easily go on from this idea to deduce the lawsgoverning the geometry of crystal faces, already empirically known. But, it would bepremature to describe this as an atomic theory of crystals. No wonder! For the scientifictheory of atoms had yet to be created, in its own good time, by the great chemists of theeighteenth century. The theorem that a lattice may be divided into unit cells, as we shouldsay today, in an infinite number of different ways would have made no physical sensewhatever to Hauy (although he would have admitted, of course, its geometricalcorrectness), since the shape of the ‘molecules soustractives’ was fixed unambiguouslyby Nature.
Thus, the true beginning of the atomic theory of crystals must be dated from a paperpublished in the year 1824 by Ludwig August Seeber, physicist in Freiburg, in Gilbert’s
8 J.R. Helliwell et al.
Annalen der Physik, Vol. 76, p. 229. Seeber, who certainly knew of Hauy’s works butprobably did not know the part we have quoted from Huygens, was trying to find anexplanation of the thermal expansion and the elasticity of solids, of which he quite rightlybelieved crystals to be the normal type. He found the brick-like structure unsuitable for hispurpose, since, he argued, the only view compatible with this picture would be that thesingle bricks themselves possess these physical properties, which does not solve theproblem but only pushes it one step farther back. Seeber, whose outlook was essentiallymodern, introduced instead the idea of a structure consisting of chemical atoms ormolecules (at the time these two concepts were not strictly differentiated), whose mutualdistances are determined by the balance of attractive and repulsive forces, thus forming asystem of stable equilibrium. External disturbances cause certain changes of position – thisis his explanation of elasticity – and possibly also elastic vibrations about the equilibriumpositions. Seeber, of course, did not visualize thermal vibration: he explained thermalexpansion in terms of the temperature dependence of the attractive and repulsive forces.In order to retain the sound parts of Hauy’s postulate, Seeber placed each of his molecules,assumed by him to be spherical, at the midpoint of the cell which would have formed oneof Hauy’s ‘molecules soustractives’; he thus arrived at a ‘parallelepipedal arrangement ofthe indivisible parts of matter’, as he describes it at the end of his paper. In our language,such an arrangement implies a primitive translation lattice, and it is not far from thisconcept to the idea that each unit cell of the space-lattice is occupied by several atoms.
This was the earliest application of the scientific atomic theory to a purely physicalproblem. The kinetic theory of gases, which is usually regarded as the beginning of atomictheory in physics, did not appear until thirty-two years later. Seeber was therefore farahead of his time, and it was no wonder that his contemporary physicists failed to respondto his ideas, which were forgotten until Sohncke revived them in 1879. But at least onemathematical problem had been raised – the number of geometrically possible space-lattices that correspond to 32 crystal classes and to their symmetry operations. MoritzLudwig Frankenheim and Auguste Bravais took up this problem, and in 1850 Bravaisdescribed the 14 pure translation lattices which have been named after him. Incidentally,his papers also contain the concept of the reciprocal lattice, which was later rediscoveredand used in connection with the study of interference effects from crystals. This purelygroup-theoretical investigation was extended by Leonhard Sohncke in 1879 through theintroduction of further symmetry operations, thus arriving at 65 different ‘space groups’.The complete solution of the problem, taking into account all possible symmetryoperations on a lattice, was given simultaneously in the year 1890 by EvgraphStepanovitsch Fedorov and by Artur Schoenflies. They derived the 230 space groupswhich are used in modern structural research.
Investigations pursued by English scientists of the following decade were lesssystematic and far more hypothetical, but their ideas possessed the advantage that theycould be visualised more easily. Inspired by the success of stereochemistry, they devisedthree-dimensional models of atomic structures based on lattices. Lord Kelvin published apaper on this subject in 1894. Reasoning along these lines was most fully expressed in aseries of long papers by W. Barlow in the last decade of the nineteenth century. Barlowtook up the idea of close packing, and distinguished for the first time correctly between thecubic and hexagonal forms of packing. He also considered the question of packing ofspheres of two or three different sizes and described, for example, the sodium chloridestructure, although neither in this nor in any other case did he, in his early papers, name asubstance which might be expected to have one of the proposed structures. This was
Crystallography Reviews 9
undoubtedly one of the reasons why the whole of his structure theory at first attractedlittle attention. Moreover, the very reality of atoms was doubted again and again right upto the end of the nineteenth century. Even in the absence of such doubts, and even whencollaboration with Pope had given the chemical application of Barlow’s theory, there wasstill no way of bringing the hypothetical structures into relation with experiment. In orderto establish structure theory on a firm basis, yet another set of ideas, those of physicaloptics, had to be brought in.
The diffraction of visible light by gratings, which mostly consisted of lines scratched onglass or metal, had already been described byGrimaldi in the seventeenth century, and againby Joseph Fraunhofer at the beginning of the nineteenth. The relevant theory can be foundin the comprehensive treatise by Friedrich Magnus Schwerd: Die Beugungserscheinungen,aus den Fundamentalgesetzen der Undulationstheorie analytisch entwickelt (1835). Thegrating was and still is the most important instrument in spectroscopy. Later physicistsengaged in work on optics have often returned to Schwerd’s theory. In particular, LordRayleigh frequently emphasized that the essential characteristic of a grating is the periodicrepetition of its elements and not the nature of those elements. Round about 1910, M. vonLaue, in writing an article on wave theory for the Encyklopadie der mathematischenWissenschaften, set himself the task of elaborating, as clearly as possible, this idea ofRayleigh’s, and arrived at an equation for the position of the diffraction maxima whichcould be extended without difficulty to the case of double periodicity as it exists in cross-gratings; in the latter case, two such equations had to be formulated.
In the meantime, the science of optics had been extended far beyond the limits of thevisible spectrum. The farthest extension on the short-wave side had come about in 1895through Rontgen’s discovery of X-rays; soon afterwards (1896), Emil Wiechert andGeorge Gabriel Stokes concluded from the way in which X-rays are produced that theymust be short waves consisting of electromagnetic pulses. This was confirmed by theobservation of their polarization, made by C.G. Barkla in 1906. Wilhelm Wien in 1907estimated their wavelength to be 7� 10�9 cm on the basis of their photoelectric effect,while A. Sommerfeld in 1912 calculated a value of 4� 10�9cm from their diffraction by aslit. On the other hand, they showed such strong quantum effects that some very eminentphysicists held firmly to the corpuscular theory of X-rays.
Both these questions and that of the fine structure of crystals were decided by thestudies of W. Friedrich and P. Knipping, which were published in the summer of 1912in the Sitzungsberichte der Bayerischen Akademie. Von Laue’s diffraction theory, whichhad provided the inspiration for those experiments and which had indeed beenconfirmed by their results, simply consisted of the diffraction conditions for a cross-grating, with the addition of a third condition to take account of the three-dimensionalperiodicity of a space-lattice. Admittedly, von Laue had expected, in accordance withthe Stokes–Wiechert pulse theory, that many more interference spots would appear onthe photographs than were actually observed, and he could only explain their absenceby ascribing to the atoms of the crystal a strongly selective scattering power for X-rays:this idea, though it later proved to be mistaken, was not altogether unreasonable inview of characteristic X-ray emission of the elements which had been found by Barkla.Towards the end of 1913, at the second Solvay Congress, von Laue used therediscovered reciprocal-lattice theory to extend to the general case of any crystal thegeometrical construction for the interference maxima from cubic crystals that had beengiven by P.P. Ewald. He thus provided the foundation for a simple ‘geometrical’ theoryof X-ray diffraction.
10 J.R. Helliwell et al.
Meanwhile, the experiments of Friedrich and Knipping, and von Laue’s interpretationof them, had become known in England, and had inspired much discussion and furtherinvestigation, particularly by W.H. Bragg and W.L. Bragg. The story of what happened ishere continued by Sir Lawrence Bragg.
‘‘In the summer of 1912 my father showed me von Laue’s paper, which had aroused hisintense interest because of his work on the exciting of the cathode rays by X-rays, whichpointed to the projectile-like properties of X-rays, and he discussed with me possiblealternative explanations for the effects which von Laue had found. I undertook someexperiments at Leeds that summer to see whether we could explain von Laue’s spots by theshooting of particles down avenues in the crystal lattice rather than by the diffraction ofwaves, experiments which were of course abortive.
‘‘On returning to Cambridge in the autumn of 1912 I studied von Laue’s photographsvery intensively, and was very naturally forced to the conclusion that they must be due todiffraction. I also concluded at the same time that one must modify the explanation ofthem which von Laue had given. Von Laue had remarked that one did not get all thespots one would expect from a simple cubic lattice, but only a selection of the wholerange. He ascribed this to the existence in the X-radiation of five characteristicwavelengths chosen so that they approximately satisfied the diffraction condition forthe spots which actually appeared in the photographs. I, on the other hand, concludedthat von Laue’s spots were due to the diffraction of ‘white’ X-radiation, representing acontinuous band of wavelengths over a certain range. I was led to this first by notingthe changing shape of the Laue spots when the distance from the photographic plate tothe crystal was altered. This, in turn, led me to consider the diffraction effect as areflection of X-ray pulses by the lattice planes of the crystal. I pointed out this wasequivalent to the selection from the continuous spectrum of a wavelength determinedby the lattice spacing of the crystal. I tested this by reflecting the X-rays from a micaplate set at a series of angles, getting in every case a spot in the reflected position andso showing, as I believed, that all wavelengths were represented over a certain range inthe X-rays. The problem then remained to explain why only certain spots appeared inthe Laue photographs, and I ascribed this to the fact that the essential underlyinglattice of the crystal was face-centred and not simple cubic. I communicated theseresults to the Cambridge Philosophical Society in November 1912. The ‘Braggequation’ appeared in this paper (p. 46) in the form �¼ 2d cos�, but in later papers �was defined as the glancing angle and not the angle of incidence.
‘‘Professor Pope at Cambridge was very interested in these results, because the closepacked lattices which he and Barlow had devised for atoms which they believed to be ofequal size were face-centred cubic. He procured crystals of potassium chloride and sodiumchloride for me and I took their Laue photographs. I showed that these could be explainedby an arrangement of alternate scattering centres in two interleaved face-centred lattices,the NaCl structure in fact, and that these centres must be equal in scattering power in KClbut different in scattering power in NaCl.
‘‘This work was done in Cambridge before I collaborated with my father. We workedalong divergent lines at first, which came together later. My father was very interested inmy explanation of the diffraction effect as a reflection, and he set up at Leeds the firstX-ray spectrometer. He was primarily interested in the nature of X-rays. He checked thatthe reflected rays were really X-rays, a point on which he wished to satisfy himself becauseof his speculations about the corpuscular nature of X-rays. He found as I did that thereappeared to be a continuous spectrum, but his spectrum also showed some peaks
Crystallography Reviews 11
superimposed upon this continuous range, and by improving the apparatus he soonnarrowed these down so much that it was clear that there were monochromaticcomponents characteristic of the target. Incidentally I think it is not often realised howmuch work he did on characteristic X-rays before Moseley made his brilliant generali-sations. My father constructed tubes with about a dozen different anti-cathodes andidentified Barkla’s K and L radiation, showing that the K contained two peaks and the Lthree peaks. He related the wavelengths to the atomic weights of the metals in each anti-cathode (the idea of atomic number had not yet come to the fore) by a simple law. In facthe gave the first hint of Moseley’s relations, and it was his work which inspired Moseley tohis broader generalisations.
‘‘My father then examined with his spectrometer crystals of KCl and NaCl such as Ihad used for my Laue photographs, and found the reflections of the characteristic peaksfrom the (100), (111) and (110) faces. It was clear at once that the spectrometer was a farmore powerful way of investigating crystal structure than the Laue photographs, which Ihad used. It was only at this stage that we joined forces. In particular, I had been trying toanalyse the diamond structure by Laue methods without success, but my father mounted iton the spectrometer and the structure became immediately obvious. We wrote a paper onthe diamond structure together, but the results which gave the clue to it were obtained byhim. I was able, however, to work along with him with the spectrometer in the summer of1913, and so to work out the structures of zinc blende, fluorspar, pyrites and some of thecarbonates, which showed how powerful the spectrometer could be. My father was at firstprincipally interested in X-ray spectra and X-ray absorption edges, but crystal structuresalso fascinated him, and from that point on, we both mainly devoted ourselves to crystalstructure analysis.’’
These experiments, together with those of Friedrich and Knipping, not onlyconfirmed von Laue’s diffraction theory but gave a direct proof of the existence of thespace-lattice, and provided a simple expression (the Bragg law) for the relationshipbetween the wavelength of the X-rays used and the lattice spacings of the crystal. Theionization curves obtained by means of the Bragg spectrometer showed clearly that the‘mirror-image reflection’ postulated by Bragg is selective and is conditioned by multipleinterference. The Bragg equation was first published in its usual form in a paper byW.H. and W.L. Bragg in the Proceedings of the Royal Society, Vol. 88, p. 428 (1913).Soon afterwards, von Laue [Physikalische Zeitschrift, 14, 421 (1913)] was able to showthat this equation was only another way of expressing the results of the geometricalspace-lattice theory.
Ionization spectrometer measurements also revealed another reason for the absence ofmany of the interference spots at first expected by von Laue. The pulse theory of X-rayspredicted much too wide an extension of their spectrum in the short-wave direction.In fact, as W. Duane and F.L. Hunt established in 1915, this spectrum ends abruptly at theshort-wavelength limit given by the now well-known quantum rule.
Still further credit is due, however, to W.H. Bragg and W.L. Bragg. X-ray diffractionpatterns had made it possible to compare the wavelengths of X-rays with the three latticeconstants, whose axial ratios were already known. Absolute measurements, however,remained impossible without a knowledge of the absolute value of the lattice constant of atleast one substance. It was necessary for this purpose to know the number of atoms in theunit cell, and this was impossible without a knowledge of the structure. The Braggs’measurements, however, had shown that sodium chloride really did possess one of thehypothetical structures postulated by Barlow. Thus, it was possible to obtain the absolute
12 J.R. Helliwell et al.
value of the lattice constant of this salt; this in turn provided an absolute measure of thewavelengths of X-rays, and hence the absolute lattice constants of all other crystalsinvestigated. Rarely has the value of hypothesis in research been so strikinglydemonstrated.
This brings us to the end of the historical introduction as far as X-rays are concerned,since all that has followed is merged into present-day practice. Yet, the space-lattice hashad another most important part to play in physics.
In 1924, L. de Broglie put forward in his Theses the basic idea of wave mechanics.In the summer of 1925, Walter Elsasser, in a letter to the editor of Naturwissenschaften,pointed out that the de Broglie waves of electrons must cause space-lattice interferenceeffects, and that experiments by Davisson and Kunzman on the reflection of electronsfrom a platinum sheet had actually shown maxima of the expected kind. When in 1926,E. Schrodinger published his communications on Quantisierung als Eigenwertproblem,C.J. Davisson and L.H. Germer began systematically to look for these effects. In March1927, they were able to publish a note in Nature to say that their efforts, made on a singlecrystal of nickel, had been crowned with success. In May of the same year, G.P. Thomsonand A. Reid announced that an electron beam of several thousand volts had, on passingthrough a celluloid film, produced Debye–Scherrer rings, and G.P. Thomson found thesame effect even more clearly with metal foils. Thus, Elsasser’s prediction was confirmedand the plainest of all proofs had been given to the connection of a wave with themovement of a corpuscle.
Admittedly, the geometrical theory of space-lattice interference does not apply sowell to electrons as it does to X-rays, especially not to low energy electrons. But it hasenjoyed further triumphs in the diffraction of neutrons, observed first by D.P. Mitchelland P.M. Powers, then since 1946 by W.H. Zinn, E. Fermi, C. Shull and otherAmerican physicists using the cyclotron or the uranium pile as a source. Here, a newpossibility has to be taken into account: the atomic structure factor, which ischaracteristic for the scattering of single atoms, may be negative as well as positive.This branch of research is, however, still in its infancy. It appears to be capable ofgreat development.
4. Short postscripts
The Nobel Prize in Physics 1914 was awarded to Max von Laue for his discovery of thediffraction of X-rays by crystals.
The Nobel Prize in Physics 1915 was awarded jointly to Sir William Henry Bragg andWilliam Lawrence Bragg for their services in the analysis of crystal structure by means ofX-rays.
The establishment of the Ewald Prize by the IUCr, for outstanding contributions tothe science of crystallography, was announced in February 1986 and was given widepublicity. The name of the Prize was chosen to recognize Professor Ewald’s significantcontributions to the foundations of crystallography and to the founding of the IUCr,especially his services as the President of the Provisional International CrystallographicCommittee from 1946 to 1948, as the first Editor of the IUCr’s publicationActa Crystallographica from 1948 to 1959, and as the President of the IUCr from1960 to 1963. A list of the IUCr Ewald Prize winners can be found at:- http://www.iucr.org/iucr/ewald-prize.
Crystallography Reviews 13
5. Concluding remarks; glimpses of the interactions between Max von Laue and William
Lawrence Bragg
In the text above written by von Laue as the Historical Introduction to the International
Tables Vol. 1, there are extensive quotes of W.L. Bragg. We can assume that very
harmonious relations existed between the two of them. This is further documented by the
following records of the award of an honorary degree to von Laue by the University of
Manchester while Bragg was Langworthy Professor of Physics there:-
14 J.R. Helliwell et al.
Crystallography Reviews 15
Reproduced with permission of the Guardian Newspaper.
6. Honouring the Centennial
The 20th Annual Meeting of the German Crystallographic Society in Munich will includea day, 12 March 2012, dedicated to a celebration of the 100th anniversary of the discovery
16 J.R. Helliwell et al.
of X-ray diffraction by Laue, Friedrich and Knipping. At its Congress in Madrid inAugust 2011, the IUCr, led by the President Prof. Dr Sine Larsen, launched thepreparations for an International Year of Crystallography (IYCr) as a Centennialcelebration of the discovery of X-ray diffraction in 1912 and the determination of the firstcrystal structures in 1913. This has now been endorsed by the Executive Committee of theInternational Council for Scientific Unions and by the Science Board of UNESCO. TheEuropean Crystallographic Association’s European Crystallographic Meetings to be heldin Bergen, Norway, in 2012 and Warwick, UK, in 2013, organized respectively by theNorwegian and British Crystallographic Associations, will feature special lectures andevents to also mark these discoveries and to endorse the IYCr.
Notes on contributors
Professor J. R. Helliwell BA (Physics, York), DPhil (MolecularBiophysics, Oxford), DSc (Physics, York), FInstP, FRSC,FSocBiol. He is, since 1989, Professor of Structural Chemistryat the University of Manchester. This photo is of the authorlecturing structural chemistry to first year bioscientists in 2009in the Rutherford Lecture Theatre of the Schuster Laboratory(the Physics Department); the bust of Lord Rutherford is visibleat right mounted on the wall. John Helliwell also workedat Daresbury Laboratory’s Synchrotron Radiation Source(SRS) from 1979 to 1993 and 2001 – 2009, whilst also a Joint
Appointee with the Universities of Keele, York and Manchester, or an Honorary Visiting Scientist,and full time as a scientific civil servant (1983–1985 and 2002). As an example of his interests in thehistory of crystallography he presented the University of Manchester 150th Anniversary ‘W L BraggLecture’ at the Schuster Laboratory in 2001. He wrote up the historical part for the ManchesterLiterary and Philosophical Society Memoirs, and which was subsequently reproduced, withpermission, in Z. Kristallogr for its 125th Anniversary. The lecture demonstrations he described inJ Appl Cryst with the video of the W L Bragg Lecture itself being accessible at the IUCr websiteeducation section. He also assisted John Blunden-Ellis of the University of Manchester Library inthe cataloguing of the Archives of Prof Durward Cruickshank FRS (1924–2007) and of Prof HenryLipson FRS (1910–1991).
Professor Alexander J. Blake BSc, PhD (both Chemistry, Aberdeen), CChemFRSC. Since 2007 he has been Professor and Director of ChemicalCrystallography at the University of Nottingham, and in the same year hewas elected Vice-President of the British Crystallographic Association.Previously he worked at the University of Edinburgh where he determinedthe crystal structures of low-melting compounds by X-ray diffraction andlater operated the Chemistry Department’s Crystal Structure Service. In 1995he moved to the School of Chemistry at the University of Nottingham. Hiscurrent research interests include high pressure crystallography and the
structural chemistry of metal-organic frameworks, both of which have involved working at theDaresbury Laboratory Synchrotron Radiation Source (SRS) and now at Diamond Light Source,and he has published over 900 papers. Professor Blake has been a lecturer (1995–2009) and theScientific Director (1999–2009) for the biennial Engineering and Physical Sciences Research Council(EPSRC)/British Crystallographic Association (BCA) Intensive Course on X-ray Structural Analysisat Durham University and has contributed to two books based on the Course. He has been aMember of the Editorial Board of Acta Crystallographica since 1995 and is currently Deputy Editorof Acta Crystallographica Section C. He is Chair of ECM28 and where a special conference sessionmarking the Centennials of Laue and the Braggs will be celebrated, and which will lead into the IYCrvery nicely. On a further historical note, he is the local custodian of boxes of Beevers Lipson strips.
Crystallography Reviews 17
John Blunden-Ellis, BSc, DpBA (Manchester), MSc (Salford) is currentlyFaculty Team Manager for Engineering and Physical Sciences in the JohnRylands University Library, University of Manchester. Previous postsinclude: Team Manager for Science Engineering & Technology in theIntute Service, Executive Secretary of the Consortium of Academic Librariesin Manchester (CALIM), and Deputy Librarian of Roche UK in WelwynGarden City. He has published a wide variety of papers largely relating toacademic librarianship and has most recently worked under the guidance ofProfessor John Helliwell in the cataloguing of the Archives of Prof Durward
Cruickshank FRS (1924–2007) and of Prof Henry Lipson FRS (1910–1991) at the University ofManchester.
Professor Moreton Moore studied mathematics and physics at Peterhouse,University of Cambridge (MA); and the physics of materials (MSc) andcrystallography (PhD) at the University of Bristol. He was awarded the DScdegree of the University of London for his publications on geometry andX-ray diffraction of diamond and semiconductors. He is the founder editorof Crystallography Reviews and he has also been Co-Editor of ActaCrystallographica A and Journal of Applied Crystallography. He wasappointed Lecturer in Physics at the Royal Holloway College, University ofLondon in 1969, working with Professor Samuel Tolansky FRS. His firstresearch investigation there was to determine if there were any diamonds in
the Apollo 11 Moon-dust. Over the years, using optical and X-ray techniques, and especiallysynchrotron radiation, he has studied imperfections in various crystals and the roles which thesedefects play in modifying the useful properties of industrial materials. He is now Emeritus Professorof Physics. Councillor Moore has also been, since 1992, an elected Independent Member ofRunnymede Borough Council and in 2006–07 he was the Mayor of Runnymede.
Professor Carl Schwalbe studied chemistry, receiving his A.B. from OberlinCollege and his A.M. from Harvard University. His PhD research at Harvardwas supervised by Nobel laureate William N. Lipscomb. After postdoctoralresearch at the Max Planck Institute for Experimental Medicine in Gottingen,Germany, he joined Aston University in Birmingham in 1972 as a Lecturer inPharmacy, eventually becoming Professor of Medicinal Chemistry. Uponretiring in 2010, he was appointed Honorary Senior Research Fellow at theCambridge Crystallographic Data Centre. His research interests involve theuse of structural information, mainly obtained by X-ray crystallography, to
explain the activity of drugs and the properties of solid dosage forms. In periods of sabbatical leaveat Brookhaven National Laboratory and Oxford University he also applied neutron diffraction andcomputational chemistry. As the editor of Crystallography News, the quarterly news magazine of theBritish Crystallographic Association, Carl Schwalbe periodically writes about significant people inthe history of crystallography, such as Carl Hermann and Charles Mauguin featured in the article onpage 24 of the December 2010 issue.
Acknowledgements
The authors are grateful to James Peters, University Archivist, John Rylands University Library,University of Manchester, for assistance with obtaining the details of the honorary DSc awarded toMax von Laue at the University of Manchester Degree Ceremony in May 1936.
18 J.R. Helliwell et al.
References
[1] Ewald, P Laue’s Discovery of X-ray diffraction by Crystals. In Fifty Years of X-ray Diffraction;Ewald, P.P., Ed.; N.V.A. Oosthoek, IUCr: Utrecht, The Netherlands, 1962; pp. 31–56, Ch. 4.
[2] von Laue, M Historical Introduction. In International Tables for X-ray Crystallography (1st ed.,1952) 2nd ed.; Henry, N.F.M., Lonsdale, K., Eds.; Kynoch Press, IUCr: Birmingham, UK, 1995;Vol. 1.
[3] University Correspondent. The Manchester Guardian (1901–1959), May 15, 1936.
Crystallography Reviews 19
